"I don't know what Jeff is doing taking shots at Donald Trump but Donald Trump has to rise above all of this and unify the party," the Wisconsin congressman -- and Trump supporter -- told CNN's Wolf Blitzer on "The Situation Room." "And by responding to the punch that Flake gave him, doesn't bring people closer together. It fissures and divides the Republican base not just in Arizona but around the country."
Duffy's call followed Trump's Sunday night tweets slamming Flake, who that morning on CNN's "State of the Union" reiterated to Jake Tapper his refusal to back the GOP standard-bearer, citing public policy stances and temperament. Trump in turn described Flake on Twitter as "weak" and "ineffective," among other insults.
On Monday Duffy said it was time for Trump to bury the hatchet so he could win over GOP loyalists, independents and soft Democrats, adding, "We don't have enough Republicans to win this race."
Addressing Trump directly, Duffy continued: "Donald, listen, don't be so sensitive. Take the hit. Let it roll off your back and, you know, look forward. Take shots at Hillary Clinton and Barack Obama if you want, but don't take shots at your own party."
Duffy conceded that Trump's highly anticipated immigration policy speech in Arizona last week did little to quell concerns some voters have with his hardline proposals.
"Well, I think we have to go with the most recent statements and I think, Wolf, that's the right decision on his part," Duffy said. "I mean, even with regard to families where you have kids that are citizens and parents who are not it makes sense to soften his position on those who are law-abiding citizens that are working hard, that are participating in the American economy."
Duffy also disagreed with Trump's response to tensions in US-Sino relations, which were on display during President Obama's trip to Hangzhou, China, for the G20 Summit this weekend.
"I don't know if that's appropriate diplomacy, packing up the plane and taking off and coming home," Duffy told Blitzer in reaction to what Trump said he would do if he were faced with the frosty reception Obama experienced in Hangzhou on Sunday. "But I also think the Chinese are trying to stick their finger in the president's eye and make him look bad and not show him due respect that a world leader."